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Physical Review Letters

Refractive Contribution to the Mass of an Elementary Excitation in a Dilute Bose-Einstein Condensate

S. V. Andreev

Published Apr 22, 2025• 1 citation
Publisher

Abstract

Since the pioneering works of Landau and Feynman, the origin of a roton minimum in the excitation spectrum of a quantum Bose liquid has been debated. A consensus has been reached on relation of the roton to eventual solidification, but this viewpoint still remains to be connected to the polaronic concept of an impurity pushing through a dense medium. The diagrammatic theory allows one to approach the problem qualitatively from a dilute limit. We revisit the equation for the elementary excitation spectrum obtained in the ladder approximation and argue that polaronic renormalization of the quasiparticle mass has a contribution due to matter-wave refraction. At low energies attenuation of the quasiparticle wave turns out to be dramatically suppressed by the condensate. Refractive correction to the mass is enhanced by Bose statistics at high momenta and produces autolocalization of an elementary excitation upon increasing the density.

DOI
10.1103/physrevlett.134.166001

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Since the pioneering works of Landau and Feynman, the origin of a roton minimum in the excitation spectrum of a quantum Bose liquid has been debated. A consensus has been reached on relation of the roton to eventual solidification, but this viewpoint still remains to be connected to the polaronic concept of an impurity pushing through a dense medium. The diagrammatic theory allows one to approach the problem qualitatively from a dilute limit. We revisit the equation for the elementary excitation spectrum obtained in the ladder approximation and argue that polaronic renormalization of the quasiparticle mass has a contribution due to matter-wave refraction. At low energies attenuation of the quasiparticle wave turns out to be dramatically suppressed by the condensate. Refractive correction to the mass is enhanced by Bose statistics at high momenta and produces autolocalization of an elementary excitation upon increasing the density.
We predict the existence of a roton-induced Bose polaron for an impurity immersed in a three-dimensional Bose-Einstein condensate with Raman-laser-induced spin-orbit coupling, where the condensate is in a finite-momentum plane-wave state with an intriguing roton minimum in its excitation spectrum. This novel polaron is formed by dressing the impurity with roton excitations, instead of phonon excitations as in a conventional (i.e., phonon-induced) Bose polaron, and acquires a significant center-of-mass momentum and highly anisotropic effective mass. We find that the roton-induced polaron evolves from a phonon-induced polaron, as the interaction between impurity and atoms increases across a Feshbach resonance. The evolution is not smooth, and a first-order phase transition from a phonon- to roton-induced polaron is observed at a critical interaction strength.
Dilute quantum gases offer a controllable platform for investigating quantum liquids, such as superfluid helium, in which correlations and fluctuations are encoded in the form of a quasiparticle energy (i.e., roton-maxon) dispersion. An approach to extracting the roton-maxon spectrum of a Bose-Einstein condensate is theoretically developed: the method relies on using an external one-dimensional optical lattice that effectively controls the response of the system, giving access to its elementary excitations.
Dipolar Bose-Einstein condensates (dBECs) exhibit a plethora of physics phenomena, from supersolidity to the rotonlike minimum in the elementary excitation spectrum. In this work we first demonstrate the existence of axis-symmetric solitary waves in (quasi-)two-dimensional dBECs: these localized excitations are characterized by quantized vortex dipoles that continuously transit to vortex-free density depletions. We then show how the presence of the roton minimum fundamentally alters the fate of such solutions when approaching Landau’s critical speed: when propagating along the polarization direction where the roton minimum occurs, the solitary wave transits into roton excitations rather than into phonons as for standard contact-interaction BECs. This finding suggests that Feynman’s hypothesis, conjectured for 3D superfluid liquid helium regarding the creation of rotons as fading vortex excitations, is valid in the context of 2D dBECs.
Dipolar Bose-Einstein condensates (dBECs) exhibit a plethora of physics phenomena, from supersolidity to the rotonlike minimum in the elementary excitation spectrum. In this work we first demonstrate the existence of axis-symmetric solitary waves in (quasi-)two-dimensional dBECs: these localized excitations are characterized by quantized vortex dipoles that continuously transit to vortex-free density depletions. We then show how the presence of the roton minimum fundamentally alters the fate of such solutions when approaching Landau's critical speed: when propagating along the polarization direction where the roton minimum occurs, the solitary wave transits into roton excitations rather than into phonons as for standard contact-interaction BECs. This finding suggests that Feynman's hypothesis, conjectured for 3D superfluid liquid helium regarding the creation of rotons as fading vortex excitations, is valid in the context of 2D dBECs.
The polaronic system consisting of an impurity in a dilute Bose-Einstein condensate is considered in the presence of a narrow Feshbach resonance. For this purpose a coupled-channel model is used, which at the mean-field level predicts the formation of quasiparticles that are a superposition of the impurity and the molecular states. The impurity-boson interactions and the coupling between the open and closed channels are then considered weak and a perturbative calculation of the corrections to the mean-field results is presented. This allows us to examine the properties of the quasiparticles, such as the lifetime and the effective mass. The relation between the model parameters and the experimental parameters is determined by identifying the low-energy TTT matrix and applying a proper renormalization scheme.
The polaronic system consisting of an impurity in a dilute Bose-Einstein condensate is considered in the presence of a narrow Feshbach resonance. For this purpose a coupled-channel model is used, which at the mean field level predicts the formation of quasiparticles that are a superposition of the impurity and the molecular states. The impurity-boson interactions and the coupling between the open and closed channels are then considered weak and a perturbative calculation of the corrections to the mean field results is presented. This allows to examine the properties of the quasiparticles, such as the lifetime and the effective mass. The model is applied to two physical systems: an impurity atom in a Bose-condensed atomic gas in 3D and a spin down lower polariton in a Bose-Einstein condensate of spin up lower polaritons in 2D. The model parameters are linked to the physical parameters by identifying the low energy T-matrix and applying a proper renormalization scheme.